非对称正态分布及广义伽马分布序列极值的极限性质

发布时间：2018-06-08 00:03

本文选题：非对称正态分布 + 广义伽马分布　；参考：《西南大学》2017年硕士论文

【摘要】：本文主要研究在最优规范常数条件下,服从非对称正态分布和广义伽马分布的独立同分布随机变量序列的极值分布以及观测值的邻近最大值的渐近性质.全文主要分为两部分:第一部分首先根据非对称正态分布的概率密度函数推导出该分布的基本性质,如Mills率,尾部表达式,并判断出该分布的极值分布类型,确定出最优规范化常数.在该规范化常数条件下,通过对尾部表达式的精确展开,得到非对称正态分布规范化最大值的极值分布的渐近展开式及其收敛到极值分布的收敛速度.其次,根据非对称正态分布的性质,判断出该分布是瘦尾分布.并确定出该分布序列观测值的邻近最大值和邻近最大值部分和弱收敛于指数分布的最优规范常数.第二部分首先在幂赋范条件下得到广义伽马分布的极值分布收敛的渐近展开式以及该分布的极值分布收敛到对应极值分布的收敛速度.其次,根据广义伽马分布的性质,判断出该分布是瘦尾分布.并确定该分布序列观测值的邻近最大值和邻近最大值部分和弱收敛于指数分布的最优规范常数.
[Abstract]:In this paper, under the condition of optimal gauge constant, we study the asymptotic properties of the extreme distribution of the sequence of independent identical variables of asymmetric normal distribution and generalized gamma distribution, as well as the asymptotic properties of the adjacent maximum values of the observed values. The paper is divided into two parts: in the first part, the basic properties of the asymmetric normal distribution, such as the Mills rate, the tail expression, and the extreme distribution type of the distribution are derived according to the probability density function of the asymmetric normal distribution. The optimal normalization constant is determined. Under the condition of the canonical constant, the asymptotic expansion of the extreme distribution of the normalized maximum value of the asymmetric normal distribution and the convergence rate of its convergence to the extreme value distribution are obtained by the exact expansion of the tail expression. Secondly, according to the properties of asymmetric normal distribution, it is determined that the distribution is a thin tail distribution. The adjacent maximum value and adjacent maximum partial sum of the observed values of the distribution sequence are determined, and the optimal gauge constants converging weakly to the exponential distribution are obtained. In the second part, the asymptotic expansion of the convergence of the extreme value distribution of the generalized gamma distribution and the convergence rate of the extreme value distribution of the generalized gamma distribution to the corresponding extreme value distribution are obtained under the condition of power normed. Secondly, according to the properties of the generalized gamma distribution, it is determined that the distribution is a thin tail distribution. The adjacent maximum value and adjacent maximum partial sum of the observed values of the distribution sequence are determined and the optimal gauge constants converge weakly to the exponential distribution.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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